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Homework 4 Q1. Suppose a consumer has utility function (u) = xy where x and y are amounts of two commodities that this consumer consume. Suppose this consumer’s income is $120, price of good x is $1/ unit and the price of good y is $4/ unit. (80 pts) 1.1) Maximize utility for this consumer. 1.2) Use the bordered Hessian to test the second-order condition.

Q2. Given the total cost function: C = x2 + 2xy + 2y2 for a firm producing goods x and y. The firm must meet a production quota of 2x + 3y = 40. (80 pts) 2.1) Minimize cost for this firm. 2.2) Use the bordered Hessian to test the second-order condition.

Q3. A consumer wants to maximize utility u (x,y) subject to the constraint PxX +PyY = B where x and y are amounts of two commodities that this consumer consume. Suppose this consumer’s income is B, price of good x is Px and the price of good y is Py. Assume that the secondorder sufficient condition is met so lHl = lJl ? 0. Find dx/dPx (80 pts)

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